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Methods of Measuring Black Hole Masses: Reverberation Mapping

Misty C. BentzGeorgia State University

Monday, September 12, 2011

Dynamical methods generally not feasible in AGNs• AGNs rare = distant, poor spatial resolution• AGNs are bright, outshine the “test particles”

Use variability instead → Reverberation mapping• relies on time resolution instead of spatial resolution

R – size of emission region V – velocity of gas in that region f – order unity scale factor

Black Hole Masses in AGNs

RM Assumptions:1. R (continuum emission region) << R (BLR)

2. time delays arise from light travel time effects3. optical continuum has simple relationship to ionizing continuum

RM does not assume any specific modelsMonday, September 12, 2011

AGN Unified Model


AGN Unified Model

Broad-line AGNs (Type 1)


AGN Unified Model

Narrow-line AGNs (Type 2)



AGN Unified ModelBlazars




AGN Unified ModelBlazars




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Inner Solar System

Orbit of Sednaaphelion = 928AU

= 5.4 light days

AGN Scales or Why It’s Hard to Study the BLR in Detail

Radius of Seyfert BLR~5 light days


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Inner Solar System

Orbit of Sednaaphelion = 928AU

= 5.4 light days

Embedded in the center of a galaxy ~40Mpc away (z~0.01)

AGN Scales or Why It’s Hard to Study the BLR in Detail


Telescope AGN

Red = continuumPurple = broad line

Measuring the BLR Radius -- RM Cartoon

BH

Broad Line Region


Telescope AGN

Red = continuumPurple = broad line

Measuring the BLR Radius -- RM Cartoon

BH

Broad Line Region

τ = 0

τ = r/c

τ = 2r/c

Average = τ = r/c


Example Data – NGC 4151

Cross-correlation → time delay of broad line response to continuum variations

Bentz et al. 2006, ApJ, 651, 775


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Time delay (cτ) → average BLR radius R

measured for ~50 AGNs

width of variable line emission → line-of-sight BLR gas velocity (V)

f includes BLR physical details (e.g., inclination, geometry, kinematics)


Woo et al. 2010

The Fudge Factor f

population average:

<f> = 5.2 +/- 1.1

Assume MBH - σ relationship is same for AGNs and

quiescent galaxies

σ difficult to measure for high-L AGNs (z > 0.1)

Morphological biases in σ measurements?


Virial Behavior in the BLR

Peterson & Wandel 2002

V ∝ Τ -1/2

where measurements exist for multiple emission lines

Bentz et al. 2010

Kollatschny 2003

Mrk110


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Consistency with Dynamical Masses

Stellar and gas dynamical measurements for 2 AGNs

with RM masses

Dynamical and RM masses are

generally consistent for NGC 4151 and

NGC 3227

More direct comparisons are needed, limited by AGN

distancesDavies et al. 2006, Onken et al. 2007,

Hicks & Malkan 2008


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Simple RM:

log MBH = 6.82 +/- 0.07(Bentz et al. 2009)

vs.

Bayesian modeling:

log MBH = 6.51 +/- 0.28 (Brewer et al. 2011)

Brewer et al. 2011

Bayesian Modeling of RM Data

Fits RM datasets with plausible BLR models

i=90defined as

face-on

Models are still simplistic

Need to study more objects


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Echo Mapping - BLR Transfer Function

Bentz et al. 2010

recovered transfer function rules out outflow

possible evidence for inflow

rotation inflow outflow


M-L relationship

AGN Lbulge from 2-D decomposition of optical

HST images

AGN M-L relationship

and

M-L relationship for only early type

quiescent galaxies

are consistent

Needs to be studied in NIR to minimize dust

AGNs

Bentz et al. 2011, in prep


Single Epoch MBH Estimates

R – L relationship yields black hole mass with one spectrum and two measurements: 1. emission line width (V) 2. AGN L → proxy for R




V




LR

V




LR

V

ALL mass estimates for AGNs using emission lines are based

on the local observed R – L relationship for Hβ


NGC 4051z = 0.00234

PG 0953+414z = 0.234

Large slit (i.e. 4”x10”) used to minimize aperture effects→ strong starlight contamination at low z

5’ x 5’ images

AGN Luminosities – Host Galaxy Starlight

Mrk 79z =0.0222


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Updates to RM DatabaseLAMP 2008

Bentz et al. 2009

MDM 2007

Denney et al. 2010

1 new object3 replacements2 additions

Hβ Results Summary:

7 new objects1 addition

Hβ Results Summary:

HST Cycle 17 WFC3 Imaging Campaign


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Updated Radius - Luminosity Relationship: Preliminary Version

New and replacement measurements in color

Bentz et al. 2011, in prep

Image

Model

Residuals


Kaspi et al. 2007

CIV R-L Relationship

Only 7 AGNs, and 5 have similar

luminosities

Slope of CIV R-L is consistent

with slope of Hβ R-L

Not enough MgII measurements for R-L relationship


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Summary

● Reverberation mapping substitutes time resolution for spatial resolution and probes the gravity of the BH

● RM masses consistent with dynamics and with Bayesian modeling

● We are just beginning to acquire data that could soon allow direct constraints on the detailed physics of the BLR gas

● The R-L relationship provides a convenient method for estimating MBH in any broad-lined AGN


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Some Big Questions:

1. What is the origin of the BLR?

2. What systematic errors are inherent in AGN black hole masses?

3. What (if any) is the role of radiation pressure in the BLR?

4. What is the range of physical characteristics (and f values) among BLRs?

5. What are the differences between the optical BLR and the UV BLR (e.g. kinematics or wind

launching)?

6. What (if any) are the physical differences between low-z and high-z AGNs?


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